A dog runs west for 20m then north for 15m. What is the resultant displacement of the dog graphically and by calculations?

15 root 2

To find the resultant displacement of the dog graphically, we can draw a vector diagram.

First, draw a line representing the dog's westward displacement of 20m. Start from an arbitrary point and extend the line towards the left.

Next, draw a line representing the dog's northward displacement of 15m. Start from the end of the previous line and extend it upwards.

The resultant displacement is the line that connects the starting point with the endpoint of the last line drawn. It represents the straight-line distance from the starting point to the endpoint.

To find the length of the resultant displacement by calculation, we can use the Pythagorean theorem.

According to the theorem, the square of the length of the hypotenuse (resultant displacement) is equal to the sum of the squares of the lengths of the other two sides (westward and northward displacements).

In this case, the length of the westward displacement is 20m, and the length of the northward displacement is 15m.

So, applying the Pythagorean theorem, we have:

Resultant displacement^2 = 20^2 + 15^2
Resultant displacement^2 = 400 + 225
Resultant displacement^2 = 625

Taking the square root of both sides, we find:

Resultant displacement = sqrt(625)
Resultant displacement = 25m

Therefore, the resultant displacement of the dog is 25m, both graphically and by calculation.